Survival outcomes, such as overall survival and progression-free survival in cancer patients, and recurrent event endpoints, such as repeated opportunistic infections in cancer patients who received hematopoietic stem cell transplantation and repeated cardiovascular events in survivors of myocardial infarction, arise naturally in clinical and biomedical studies. It is important to identify individuals who are at a high risk of experiencing failure events so that these individuals can be targeted for more intensive monitoring and treatment. The objective of this project is to develop efficient and statistically proper methods to better model, estimate, and predict the risk of survival and recurrent event outcomes. The proposed statistical methods either provide new frameworks, offer solutions to problems where existing methods are either not available or are known to be inappropriate, or improve over existing methods. Under Aim 1, we develop new approaches for combining information from the individual- level data and aggregated survival information from external sources so that efficient estimation of the effects of interest and more accurate risk prediction fr the failure event can be achieved. The proposed approaches are very flexible in the sense that they can automatically combine survival information for different subgroups and the information may be derived from different studies. Under Aim 2, we propose non-restrictive semi parametric models and develop new approaches to deal with important analytical issues arising in the analysis of univariate and bivariate recurrent event data. The proposed approach can better characterize the effects of a treatment or risk factors and properly evaluate patients' quality of life beyond the first clinical event. Moreover, monitoring strategies and prophylaxis regimens can be tailored according to patients' risk problem based on the recurrent event models. Under Aim 3, we develop a novel binomial likelihood inference procedure for the additive hazards model which focuses on modeling the difference in the risk of failure events. The proposed methods are expected to be efficient and produce proper probability estimates even when sample size is small. Hence they will be particularly useful for the purpose of risk prediction. Th R package developed under this aim will further promote the use of additive hazards model in survival analysis. Under Aim 4, we investigate the bias induced by the ad-hoc last-observation-carried-forward approaches in the recurrent event data analysis, and propose a simple semi parametric estimation procedure that properly handles the covariate information collected at regular visits and that collected at recurrent event times to obtain consistent estimation. The proposed research holds both methodological significance and scientific significance. First, the proposed methodology has broad applicability in clinical and biomedical studies where survival and recurrent event outcomes are common endpoints. Second, for each aim, user-friendly software will be made freely available for public use. Finally, the proposed research holds the potential to advance the understanding of disease progression and to gain new knowledge about the long-term effects of treatment and intervention strategies on recurrent adverse events and mortality.